If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are

If $\sin \theta + \cos \theta = 1$ then the general value of $\theta $ is

If $\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$ is the solution of $4 \cos \theta+5 \sin \theta=1$, then the value of $\tan \alpha$ is

Number of principal solution of the equation $tan \,3x - tan \,2x - tan\, x = 0$, is

Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$  If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal

If the solution for $\theta $ of $\cos p\theta + \cos q\theta = 0,\;p > 0,\;q > 0$ are in $A.P.$, then the numerically smallest common difference of $A.P.$ is